Question

Fibonacci numbers Take 10 numbers as shown below:
a, b, (a + b), (a + 2b), (2a + 3b), (3a + 5b), (5a + 8b), (8a + 13b), (13a + 21b), and (21a + 34b). Sum of all these numbers = 11(5a + 8b) = 11 × 7th number.
Taking a = 8, b = 13; write 10 Fibonacci numbers and verify that sum of all these numbers = 11 × 7th number.

Answer 1

Given:
$a=8andb=13$
The numbers in the Fibonnaci sequence are arranged in the following manner:
$1st,2nd,(1st+2nd),(2nd+3th),(3th+4th),(4th+5th),(5th+6th),(6th+7th),(7th+8th),(8th+9th),(9th+10th)$

The numbers are $8,13,21,34,55,89,144,233,377\mathrm{and}610$.
Sum of the numbers = ​$8+13+21+34+55+89+144+233+377+610$
$=1584$
$11\times 7thnumber=11\times 144=1584$